Why is the validation loss less than the training loss, and what can be said about the effect of the learning rate?
This is very difficult to tell with the information provided, but the phenomenon  is something that I have encountered many times before. Sometimes this is not a bad thing, here are some possible considerations/explanations:

Data from the training set could be identical or leaking in to the validation set.
Using a high dropout rate can cause this as well as other generalization techniques.
The training set may contain outliers, contributing to higher loss and difficulty in learning.

Also, note that the there is not so much an issue with the training loss bouncing around as long as it decreases over time. You may want to try different optimizers as well to see if that changes this behavior.